Question

Use the sample data and confidence level given below to complete parts a through d. A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1069 and x=557 who said yes.

Use a 99% confidecne level.

A. find the best point of estimate of the population of portion p.

B. Identify the value of the margin of error E. E= round to four decimal places as needed.

C. Construct the confidence interval. _ < p <_ round to three decimal places.

D. Write a statement that correctly interprets the confidence interval.

Answer 1

a) The best point estimate of the population proportion here is computed as:
p = x/n = 557 / 1069 = 0.5210
Therefore 0.5210 is the required point estimate here

b) For 99% confidence level, we have from the standard normal tables:
P(-2.576 < Z < 2.576) = 0.99

Therefore the margin of error here is computed as:

$MOE = z^*\sqrt{\frac{p(1-p)}{n}} = 2.576*\sqrt{\frac{0.5210(1 - 0.5210)}{1069}} = 0.0394$

Therefore 0.0394 is the margin of error here.

c) The confidence interval therefore is obtained here as:

$p \pm MOE$

$0.5210 \pm 0.0394$

This is the required 99% confidence interval here.

d) The interpretation of this is that we are 99% confident that the true population proportion lies within the above obtained confidence interval here.